# How do you do simplify sin [2 tan^-1 (-2)]?

Apr 19, 2016

$- \frac{4}{\sqrt{5}}$.

#### Explanation:

Let a = tan^(-1)(-2.

$\tan a = - 2$.

As tan a is negative , sin a and cos a have opposite signs.
So, $\sin a = \pm \frac{2}{\sqrt{5}}$ and, correspondingly,$\cos a = - \frac{1}{\sqrt{5}} \mathmr{and} \frac{1}{\sqrt{5}}$.
The given expression is $\sin 2 a = 2 \sin a \cos a = - \frac{4}{5}$.